The homology of ``\(k\)-equal'' manifolds and related partition lattices
type: Item
instance of: scholarly article
title: The homology of ``\(k\)-equal'' manifolds and related partition lattices
zbMATH Open document ID: 0845.57020
author: Volkmar Welker
author: Anders Bjoerner
published in: Advances in Mathematics
publication date: 1996-09-16T00:00:00Z
review text: This paper analyzes the topology of the spaces \(V(n,k)\) consisting of sets of points \((x_1,\dots, x_n)\) in \(\mathbb{R}^n\) (or \(\mathbb{C}^n\)) which satisfy \(x_{x_1} = x_{i_2} = \dots = x_{i_n}\) for some set of \(k\) indices, and \(M(n,k) = \mathbb{R}^n - V(n,k)\) (or \(\mathbb{C}^n - V(n,k)\)). The \(M(n,k)\) are the ``\(k\)-equal'' manifolds of the title. For \(k = 2\), these spaces have been much studied, so the emphasis is on larger \(k\) values. The results generally say that the cohomology is free abelian, and the ranks are determined.
Mathematics Subject Classification ID: 57R19
Mathematics Subject Classification ID: 52C35
Mathematics Subject Classification ID: 06A11
zbMATH DE Number: 745285
zbMATH Keywords: arrangements of hyperplanes
zbMATH Keywords: partition lattice
zbMATH Keywords: manifolds
zbMATH Keywords: cohomology
MaRDI profile type: Publication
full work available at URL: aima.1995.1012
OpenAlex ID: W2030112334
DOI: 10.1006/AIMA.1995.1012
description: scientific article; zbMATH DE number 745285